| Region | Grads 25-34 | Grads 45-54 | All Grads |
|---|---|---|---|
| Europe | 128 | 147 | 138 |
| Nordics | 107 | 121 | 114 |
| Pacific | 147 | 186 | 167 |
| USA | 162 | 169 | 169 |
444 Lecture 24
2024-04-11
Relative wage by educational attainment
| Region | Grads 25-34 | Grads 45-54 | All Grads |
|---|---|---|---|
| Europe | 128 | 147 | 138 |
| Nordics | 107 | 121 | 114 |
| Pacific | 147 | 186 | 167 |
| USA | 162 | 169 | 169 |
‘Nordic’ here is Norway, Sweden, Finland, Denmark; ‘Europe’ is rest of Europe; ‘Pacific’ excludes USA.
For most of these facts we can get very resilient data cross-nationally.
But there’s one group, which will be important in what follows, for which we really have to focus on US data.
That’s the ‘some college’ group.
Educational Attainment in the US (wiki)
https://www.bls.gov/emp/chart-unemployment-earnings-education.htm
US weekly pay by educational attainment. Actually a little over million dollar bonus for college grads
| Level | Proportion | Median Pay |
|---|---|---|
| High School | 28.5% | $853 |
| Some College | 16% | $935 |
| Associate | 10% | $1,005 |
| Bachelors | 22% | $1,432 |
| Masters | 9.5% | $1,661 |
Ideally we should
Well, three plus/minus one:
And one extra (that may be one of the last two)
College develops skills, and those skills are valuable.
Employers are rationally willing to pay for employees with those skills.
Students develop those skills because the (appropriately discounted) returns from developing them are larger than the costs of developing the skills.
First, not everyone would develop skills by going to college, so not everyone should go.
For some people, going to college would be like building a fancy house next to a bunch of factories - not a good use of the land. (And that’s true even if the land might be very valuable, just not in the way that is enhanced by a fancy house.)
Second, when we say college develops skills, we don’t mean that lectures develop skills. College also includes:
Should be a bit careful about the last couple of points.
I can see (dimly) how the stuff we’re covering in 444 could be valuable for employers.
But the last big course I taught had a long unit on medieval epistemology, which I think is really philosophically valuable, but I have no idea how it leads to increased profits for an employer hiring someone who took the course.
And a commonly expressed worry is that lots of courses are like this.
In reply, one might note that a lot of college courses set grads up with skills that come in useful in unexpected ways.
For instance, I’m told the people who are getting the best results out of image generating software are art history majors who have a better understanding of the ways in which pictures have been put together over the centuries.
In general, by not optimising for the present, we might produce good long term value.
If you go to a UM soccer match, where tickets are like $5, there is someone carefully checking the tickets.
On the human capital model, you’d think this lecture was much more valuable than a soccer match.
But there are no ticket collectors at the door. Anyone could walk in! We don’t act like it is some special value.
On the other hand, we don’t grade just anyone’s work, and we do restrict entry to the dorms.
If the lectures are a small part of the way in which we add skills, this might all make sense.
This is the name for the premium people get for finishing a college degree.
It is really substantial.
On the human capital model, you’d think that 3 years of college would get you 3/4 of the skill acquisition of 4 years of college.
But you really, really don’t see that in the wage data.
This is an objection to the human capital effect being all of the explanation for the college wage premium.
We’ll want to be careful as we proceed about distinguising:
Not everyone gets admitted to fancy colleges. Here’s a model for the college wage premium.
The strongest version of this theory is that this explains 100% of the college wage premium.
I think (for reasons I’ll soon get to) that is pretty implausible.
A weaker version is that it explains some of the college wage premium. And it would be surprising if it explained nothing.
Some colleges admit most applicants; some colleges admit all applicants.
These colleges do (as far as I can tell) have a smaller wage premium than Michigan or similarly selective schools.
But they do still have a premium, and the selection model can’t explain this.
The strongest version of this theory is that it’s just the admission of getting into college that’s evidence you’ll get a high paying job.
If that were true, we’d expect to see a very different world to the one we actually see.
Why does admission to college mean you’ll get a high paying job?
Spence gives an example where lots of variables are continuous.
We’re going to use a much simpler example, where the variables are binary.
This will obviously mean much less realism, but I think it doesn’t change the important strengths and weaknesses of the model. (As long as we don’t fuss about details.)
Though if you think I’m being too fair (or more likely too unfair) to the model for this reason, say so!
For Employer it’s easy
For Worker it’s a bit trickier
| Nature | Worker | Employer | Work-Pay | Emp-Pay |
|---|---|---|---|---|
| High | College | Good | 3 | 1 |
| High | College | Poor | -1 | 0 |
| High | Beach | Good | 4 | 1 |
| High | Beach | Poor | 0 | 0 |
| Low | College | Good | -1 | 0 |
| Low | College | Poor | -5 | 1 |
| Low | Beach | Good | 4 | 0 |
| Low | Beach | Poor | 0 | 1 |
Figure 1: College or Beach game
This tree has a separating equilibrium:
The model is obviously silly in some ways.
Solves all the problems of previous models:
It’s really inefficient! The best workers in your workforce spending 4 years doing nothing useful just as a sorting device.
Why does the college wage premium rise with age?
The college wage premium is over one million dollars.
The model requires that college is more costly for Low workers than High workers.
There’s an annoying terminological point here. Different people use the phrase ‘honest signal’ in different ways. Some people use it for any situation where there is a separating equilibrium. I prefer using it for games like the following.
Low can’t go to college. At least, they can’t finish it.
Everything else in the graph is the same. So here’s the revised tree.
Figure 2: Honest College or Beach game
If we have time (we probably won’t) I’ll talk through how these models are used in biology.
The general idea is that sometimes it is worth doing something to signal, perfectly reliably, that you can do it.
This gets rid of the third problem - it’s not that Low refuses to take the million dollar bonus, it’s that they can’t.
I’m not sure it helps with the other three, but on the other hand, I thought that was the biggest problem with the first model.
This model has some features in common with the selection model.
What makes someone get a Good job is the same thing that causes them to (be able to) finish college: namely, that they are a High.
Which is most likely in your view to be most of the explanation of the college wage premium.
We’ll swing back to somewhat traditional epistemology, looking at how philosophers in the last decade or so have used some of the tools we’ve seen in this course to get a better understanding of